Newton polygon and string diagram

TL;DR

This paper explores the relationship between the graph-like images of curves under moment maps and their Newton polygons, with applications to Lagrangian torus fibrations in Calabi-Yau manifolds.

Contribution

It introduces a novel connection between moment map images and Newton polygons, advancing understanding of Lagrangian fibrations in Calabi-Yau geometry.

Findings

Established a link between graph images and Newton polygons.

Applied the relationship to Lagrangian torus fibrations.

Provided new insights into Calabi-Yau manifold structures.

Abstract

In this work, we discuss graph like image of curves under moment maps and their relation with the Newton polygon of the curve, which has applications to Lagrangian torus fibration of Calabi-Yau manifolds.